Hilton Head/Savannah that cater to food allergies?

We'll be taking a vacation on Hilton Head for the first time in a few weeks at Disney Vacation Club. I just discovered they don't offer a sit-down restaurant, which is terrible because Disney is one of the only places I really trust with my food allergies when dining out.

Does anyone know of any NON-CHAIN restaurants in the Hilton Head/Savannah area that either cater to people with food allergies, or cook with local, organic or whole foods rather than frozen, prepackaged burgers, or pre-marinated meats, etc.?

We plan on going grocery shopping on the island at Fresh Market (and any veggie stands we find) and can cook most meals in our room, which has a kitchen. But for days when we're sight seeing, would like to bring a list of safe places to eat.

My allergies are legume/soy/nuts, so Asian is out (don't want to take chances with that one) - but seafood, steak, Italian, etc. is great. Thanks in advance!!